definition plus : nat \to nat \to nat \def
-let rec plus (n,m:nat) \def
- match n:nat with
+let rec plus (n,m) \def
+ match n with
[ O \Rightarrow m
| (S p) \Rightarrow S (plus p m) ]
in
qed.
definition times : nat \to nat \to nat \def
-let rec times (n,m:nat) \def
- match n:nat with
+let rec times (n,m) \def
+ match n with
[ O \Rightarrow O
| (S p) \Rightarrow (plus m (times p m)) ]
in
qed.
definition minus : nat \to nat \to nat \def
-let rec minus (n,m:nat) \def
- [\lambda n:nat.nat] match n:nat with
+let rec minus (n,m) \def
+ [\lambda n:nat.nat] match n with
[ O \Rightarrow O
| (S p) \Rightarrow
- [\lambda n:nat.nat] match m:nat with
+ [\lambda n:nat.nat] match m with
[O \Rightarrow (S p)
| (S q) \Rightarrow minus p q ]]
in
qed.
definition leb : nat \to nat \to bool \def
-let rec leb (n,m:nat) \def
- [\lambda n:nat.bool] match n:nat with
+let rec leb (n,m) \def
+ [\lambda n:nat.bool] match n with
[ O \Rightarrow true
| (S p) \Rightarrow
- [\lambda n:nat.bool] match m:nat with
+ [\lambda n:nat.bool] match m with
[ O \Rightarrow false
| (S q) \Rightarrow leb p q]]
in leb.
intro.
intro.
intro.intro.
-normalize goal at (? ? % ?).
+STOP normalize goal at (? ? % ?).